The axion mass is determined by the ratio of the soft breaking masses \(m_{ij}^{(\prime )2}\)  and the decay constant \(f_a\) , as described in Sec. . The mass spectrum of the extra Higgs bosons also depends on the soft breaking masses \(m_{ij}^{(\prime 2)}\) . This implies that for a given decay constant, the axion mass can be related to the mass spectrum of the heavy Higgs bosons. To see if this picture is correct, we study the implications of the XENON1T excess in the electron recoil event [1]} for the 3HDM with the \(B-L\)  Higgs bosons.
We will examine the parameter region which explains the XENON1T
excess and satisfies all the constraints presented in the previous section.
